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Mathematical Physics

Title:
From Pure Spinor Geometry to Quantum Physics: A Mathematical Way

Abstract: In the search of a mathematical basis for quantum mechanics, in order to
render it self-consistent and rationally understandable, we find that the best
approach is to adopt E. Cartan's way for discovering spinors; that is to start
from 3-dimensional null vectors and then show how they may be represented by
two dimensional spinors. We have now only to go along this path, however in the
opposite direction; with these spinors (which are pure) construct bilinearly
null vectors: and we find that they naturally generate null vectors of
Minkowski momentum space, where Cartan equations defining pure spinors are
identical to all equations of motion for massless systems: both the quantum
(Weyl's) and the classical ones (Maxwell's), are determined by them. We have
then the possibility of a new, purely mathematical, determination of h: the
Planck's constant, and thus the possible mathematical starting point for the
representation of quantum mechanics.